|By Carmel Crimmins

DAVOS (Reuters) - Top bankers are confident that British Prime Minister Theresa May's government will support a transition period of several years for the financial sector to cope with Britain's exit from the European Union.

May met the heads of major U.S. financial firms at the World Economic Forum in Davos on Thursday to discuss their concerns.

The Prime Minister confirmed on Tuesday that Britain would quit the single market when it exits the EU, although she said she would back an "implementation" period..

Financial firms have accepted that they will lose their 'passporting' rights to freely sell services across the 28-nation bloc after Brexit, but want more time to adapt to whatever terms are agreed with the EU.

"I think the government does [support it] because I think they understand the complexity of this," Barclays <BARC.L> Chairman John McFarlane, who is also chair of financial industry lobby group TheCityUK, told Reuters earlier on Thursday.

A source familiar with the talks in Davos, which included executives from Goldman Sachs <GS.N> and Morgan Stanley <MS.N>, said May had been receptive to their points on transition.

"All the banks want a multi-year agreement. She seemed to understand that. They talked about changing the name from 'transitional' arrangement to something that was less open for negotiation," the source said.

Brexit minister David Davis said on Wednesday companies will have a maximum of a two-year transitional deal to help smooth Britain's exit from the EU after 2019, although May said Tuesday the length of any such deal may vary for different industries.

That could fit with what British bankers are calling for.

"We want a standstill arrangement for three years, that would kick in after the government's negotiations on Brexit are finalised," McFarlane said.

GROWTH AT STAKE

Bank of America <BAC.N> chief executive Brian Moynihan told Reuters that May had made it clear in her speech on Tuesday that she wanted to get Brexit right by allowing enough time for implementation, adding that banks now need to persuade the EU that economic growth could be at stake without a transition.

"We as an industry have got to get that message across because you don't want to disrupt the economies that are now starting to grow a little bit, you don't want to disrupt the free flow of capital, you don't want to disrupt people's lives," Moynihan said.

Meanwhile, international and British banks, insurers and asset managers are seeking a bespoke deal with Europe that would give 'mutual recognition’ to as many of their products and services as possible, McFarlane said.

And while UBS <UBSG.S> and HSBC <HSBA.L>, two of Europe's biggest banks, warned that they could each move about 1,000 jobs out of London, Barclays will keep the bulk of its activities in Britain after Brexit, its chief executive Jes Staley told the BBC on Thursday.